G is the group 243gp37
G has 3 minimal generators, rank 4 and exponent 3. The centre has rank 2.
The 13 maximal subgroups are: E27xC3 (12x), V81.
There are 10 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 3, 3, 3, 3, 3, 3, 3, 3, 3, 4.
At present no information on the cohomology ring.